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McGraw Hill Integrated II, 2012 View details

6. Surface Areas and Volumes of Spheres

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Exercise 13 Page 852

To find the area of a hemisphere, calculate the area of half of a sphere with the same radius and add the area of the great circle.

680.9in.^2

Practice makes perfect

A hemisphere is half of a sphere.

To find the area of a hemisphere we need to calculate the area of half of a sphere with the same radius and add the area of the great circle. Surface Area of a Hemisphere [0.8em] A=1/2(4π r^2)+π r^2 We first need to calculate the radius. To do so we will consider the given fact that the diameter is the radius two times. d=2r We can substitute 17 inches for d in this formula and solve for the radius r.

d=2r

Substitute

d= 17

17=2r

DivEqn

.LHS /2.=.RHS /2.

8.5=r

RearrangeEqn

Rearrange equation

r=8.5

We know that r=8.5inches. We can substitute this value into the formula for the area of a hemisphere and simplify.

A=1/2(4π r^2)+π r^2